Movement and Diffusion of the Helium Atom in Nanostructures (in Pores) with Water

The influence of water-filled nanoscale defects on the total movement of helium atoms through a quartz crystal is considered. The approximation of local chains is used, the interaction constant of which characterizes the interaction of the helium atom with the environment. The appearance of water molecules in defects (pores) leads to the renormalization of this interaction. The D'Alembert principle is used to evaluate this renormalization. The effect of such a renormalization of the interaction on the diffusion coefficient of helium through a crystal with defects filled with water is considered.

A General Numerical Scheme for the Optimal Control of Fractional Birkhoffian Systems

This paper deals with the optimal control of fractional Birkhof-fian systems based on the numerical method of variational integrators. Firstly, the fractional forced Birkhoff equations within Riemann–Liouville fractional derivatives are derived from the fractional Pfaff–Birkhoff–d'Alembert principle. Secondly, by directly discretizing the fractional Pfaff–Birkhoff–d'Alembert principle, we develop the equivalent discrete fractional forced Birkhoff equations, which are served as the equality constraints of the optimization problem. Together with the initial and final state constraints on the configuration space, the original optimal control problem is converted into a nonlinear optimization problem subjected to a system of algebraic constraints, which can be solved by the existing methods such as sequential quadratic programming. Finally, an example is given to show the efficiency and simplicity of the proposed method.

Kinematic characteristics of the car movement from the top to the calculation point of the marshalling hump

Introduce analytical acceleration formulas that are derived from the classic d'Alembert principle of theoretical mechanics for high-speed sections and sections of retarder positions; show the possibility of determining the instantaneous car speeds in each section of the marshalling hump according to the formulas of elementary physics both for high-speed sections and for sections of retarder positions; provide formulas for determining the time of movement of a car with uniformly accelerated and/or uniformly retarded motion of the car on the inclined part of the hump, as well as in areas of retarder positions. Research methods: The classic d'Alembert principle of theoretical mechanics is widely used in the paper. Main results: For the first time, the results of constructing a graphical dependence of the estimated height of the marshalling hump over the entire length of its profile are presented in the form of a decrease in the profile height of each section of the inclined part in proportion to the slope of the track. The results of constructing graphical dependences on changes in the speed and time of movement of a car along the entire length of the inclined part of the marshalling hump are fundamentally different from the existing methodology, where, for example, curves of medium (rather than instantaneous) speeds of a car are built. The proposed new methodology for calculating the kinematic characteristics of the car movement along the entire length of the hump allows an analysis of the mode of shunting car at the marshalling humps.

Vibration analysis of the oscillation support of column load cells in low speed axle-group weigh-in-motion system

Under the condition of dynamic weighing, the support types of the column load cells can be divided into elastic support and oscillation support. The weighing system with oscillation support shows significant vibration characteristics, which affects the weighing accuracy and the fatigue life of the load sensor. In this paper, the dynamic characteristics of the oscillation supporting column load cell in low speed axle-group weigh-in-motion system are analysed. It is found that the restoring force of the oscillation support is approximately proportional to the oscillation angle and the applied vertical load. The dynamic equation of the oscillation support vibration of the column load cells established by means of d’Alembert principle. The numerical calculations of the dynamic response of the weighing system with oscillation support are carried out in the free state and dynamic weighing state respectively. The factors affecting the amplitude and recovery time of the support vibration are obtained. This study provides a reference for the analysis of the dynamic weighing accuracy.

Variational integrators for stochastic dissipative Hamiltonian systems

Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian, which approximates a type-II stochastic generating function for the stochastic flow of the Hamiltonian system. The generating function is obtained by introducing an appropriate stochastic action functional and considering a stochastic generalization of the deterministic Lagrange–d’Alembert principle. Our approach presents a general methodology to derive new structure-preserving numerical schemes. The resulting integrators satisfy a discrete version of the stochastic Lagrange–d’Alembert principle, and in the presence of symmetries, they also satisfy a discrete counterpart of Noether’s theorem. Furthermore, mean-square and weak Lagrange–d’Alembert Runge–Kutta methods are proposed and tested numerically to demonstrate their superior long-time numerical stability and energy behaviour compared to nongeometric methods. The Vlasov–Fokker–Planck equation is considered as one of the numerical test cases, and a new geometric approach to collisional kinetic plasmas is presented.

A New Approach in Analytical Dynamics of Mechanical Systems

This paper presents a new approach to the advanced dynamics of mechanical systems. It is known that in the movements corresponding to some mechanical systems (e.g., robots), accelerations of higher order are developed. Higher-order accelerations are an integral part of higher-order acceleration energies. Unlike other research papers devoted to these advanced notions, the main purpose of the paper is to present, in a matrix form, the defining expressions for the acceleration energies of a higher order. Following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), the equations of the dynamics of fast-moving systems include, instead of kinetic energies, the acceleration energies of higher-order. To establish the equations which characterize both the energies of accelerations and the advanced dynamics, the following input parameters are considered: matrix exponentials and higher-order differential matrices. An application of a 5 d.o.f robot structure is presented in the final part of the paper. This is used to illustrate the validity of the presented mathematical formulations.

Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors

The present paper recalls a formulation of non-conservative system dynamics through the Lagrange–d’Alembert principle expressed through a generalized Euler–Poincaré form of the system equation on a Lie group. The paper illustrates applications of the generalized Euler–Poincaré equations on the rotation groups to a gyrostat satellite and a quadcopter drone. The numerical solution of the dynamical equations on the rotation groups is tackled via a generalized forward Euler method and an explicit Runge–Kutta integration method tailored to Lie groups.

KINETOSTATIC ANALYSIS FOR FOUR-BAR LINKAGE MECHANISM OF PROSTHETIC KNEE JOINT

In this paper, a mathematical model of four-bar linkage mechanism is built to investigate the prosthetic knee joint, by means of the bar group method, and the motion of the prosthetic knee joint is simulated by motion analysis software. In the state of motion of the four linkage mechanism, to the moving component of the mechanism, the relationship between the moving displacement, velocity and acceleration are obtained. On the basis of the above investigation, dynamic statics analysis for the moving component of four-bar linkage mechanism are completed by the ‘D’Alembert principle. The research results show that, with the change of the rotating angle of the active part, the counter-force of rotating pair and the balance torque on active component are all changeable, which will provide a theoretical basis for the design of prosthetic knee joint mechanism with longer life and better damping effect.

Design, Modeling, and Motion Analysis of a Novel Fluid Actuated Spherical Rolling Robot

This paper studies a novel fluid actuated system for a spherical mobile robot. The robot’s mechanism consists of two essential parts: circular pipes to lead spherical moving masses (cores) and an internal driving unit to propel the cores. The spherical shell of the robot is rolled by displacing the cores in the pipes filled with fluid. First, we describe the structure of the robot and derive its nonlinear dynamics using the D’Alembert principle. Next, we model the internal driving unit that actuates the core inside the pipe. The simulated driving unit is studied with respect to three important parameters—the input motor torque, the actuator size, and the fluid properties. The overall model of the robot is then used for analyzing motion patterns in the forward direction. Analytical studies show that the modeled robot can be implemented under the given design specifications.